Question

give the coordinates of the vertices of triangle ghi under a dilation about the origin with scale factor of \\(\frac{3}{2}\\).
\\(g\\ (8, 11)\\)
\\(h\\ (-12, 7)\\)
\\(i\\ (-12, -9)\\)
show your work here
\\(g =\\)
\\(h =\\)
\\(i =\\)

Explanation:

Step1: Dilate point G

To dilate a point \((x, y)\) about the origin with scale factor \(k\), we use the rule \((x, y) \to (kx, ky)\). For \(G(8, 11)\) and \(k = \frac{3}{2}\), we calculate \(x\)-coordinate: \(8\times\frac{3}{2}=12\) and \(y\)-coordinate: \(11\times\frac{3}{2}=\frac{33}{2}\). So \(G'=(12, \frac{33}{2})\).

Step2: Dilate point H

For \(H(-12, 7)\) and \(k = \frac{3}{2}\), \(x\)-coordinate: \(-12\times\frac{3}{2}=-18\) and \(y\)-coordinate: \(7\times\frac{3}{2}=\frac{21}{2}\). So \(H'=(-18, \frac{21}{2})\).

Step3: Dilate point I

For \(I(-12, -9)\) and \(k = \frac{3}{2}\), \(x\)-coordinate: \(-12\times\frac{3}{2}=-18\) and \(y\)-coordinate: \(-9\times\frac{3}{2}=-\frac{27}{2}\). So \(I'=(-18, -\frac{27}{2})\).

Answer:

\(G' = (12, \frac{33}{2})\)
\(H' = (-18, \frac{21}{2})\)
\(I' = (-18, -\frac{27}{2})\)